Tree Diagram Tree Diagram A diagram used in strategic decision making, valuation or probability calculations. The diagram starts at a single node, with branches emanating to additional nodes, which represent mutually exclusive decisions or events. In the diagram below, the analysis will begin at the first blank node. A decision or event will then lead to node A or B. From these secondary nodes, additional decisions or events will occur leading to the third level of nodes, until a final conclusion is reached. The probability is useful way of information in which the event will occur or happened. This can takes value between 0 and 1. We can express the thought of probability by using tree diagrams. Graphic representation should be using in formative of sample space for an experiment and for computing probabilities. This is known as tree diagrams using of probability. Here we will discuss about how to using tree diagrams in probability. Tree diagram is the easiest way to solve the probability problems.Tree diagram shows the outcome of any event.This is used for giving the all possible possibilities which is also called the Sample space.And the each leaf in the tree represents a outcome of any events.
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Events may be of any type whether a single event may be composite of more than one event.This composite events are supposed to be called as compound event. And in the drawing of the tree diagram it is not required to concentrate on the type of event the flow of diagram will be same. As the tree diagram is made irrespective kind of event so it is very easy to make.The sample space of any particular event can be obtained by looking at the whole sample space. Example 1: 12 painted spot in a set Four numbers of Blue, Two numbers of White, Five numbers of Red. One should be taken and color noted, go back to set, then a second taken. What is the probability using tree diagram? Solution: Given, Blue = Four numbers White = Two numbers Red = Five numbers Here, we are representing the Blue, White and red colours with the symbols of B, W and R. Example 2: What is the possible outcomes when the coin should be tossing two number of times? Solution:
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Given, we are tossing a coin in two times. The possible outcomes for this problems are, {Head, Head}, {Head, Tail}, {Tail, Head} and {Tail, Tail} When we using the tree diagram for this outcomes, it will look like below picture.
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